Background: Visual Studio code releases are often slightly behind Typescript releases. For example, Typescript 1.6 (with JSX/TSX support) was released in 2015-09-11, but as of 2015-09-29, VSCode hadn't been updated to use Typescript 1.6.
You can, however, force VSCode to use the latest version of Typescript (tsc / tssserver). Let's assume you have Typescript installed globally via npm, i.e. you've run:
npm install -g typescript
Then it's mostly likely been installed in: